without _Y(t) and DESol?

f := diff(u(t), t$2) + (2/t-1/t^2*p(1/t))*diff(u(t),t) + 1/t^4*q(1/t)*u(t) = 0;
dsolve(f,u(t));
u(t) = DESol({q(1/t)*_Y(t)/t^4+(2/t-p(1/t)/t^2)*(diff(_Y(t), t))+diff(_Y(t), t, t)}, {_Y(t)})

just would like to find u1 and u2 solution

how to transform this differential equation with a substitution?

f := diff(u(x),x$2) + p(x)*diff(u(x),x)+q(x)*u(x)=0;
transformed := subs(x=1/t, f);

f := diff(u(x),t$2)*diff(t,x$2) + p(x)*diff(u(x),t)*diff(t,x)+q(x)*u(x)=0;

diff(1/t,t);
diff(1/t,t$2);

x = 1/t
dx/dt = -1/t^2
d2x/dt2 = 2/t^3

d2u/dt2*dt2/dx2
du/dt*dt/dx
diff(u(t),t$2)*1/(2/t^3) + p(t)*diff(u(t),t)*1/(-1/t^2)+q(t)*u(t)

restart;
f := u2*1/(2/t^3) + p(t)*u1*1/(-1/t^2)+q(t)*u;
f2 := collect(f/t^3*2, {u2, u1, u});
subs(u2 = diff(u(t),t$2), subs(u1 = diff(u(t), t), subs(u=u(t), f2)));

but not equal to below which is in book, is this equation wrong in book?

f := diff(u(t), t$2) + (2/t-1/t^2*p(1/t))*diff(u(t),t) + 1/t^4*q(1/t)*u(t) = 0;

how to do optimization for two equations in terms of two variables

LPSolve({eq1}, {eq2}, assume = {nonnegative});

eq1 is a rational function and eq2 is a very large rational function

after run , it return error, objective function must be specified as a linear polynomial or vector

da := [LengthSplit(Flatten([[1,m],[2,m2],[seq([i+1,close3[i][1]], i=2..4)]]),2)];
f := PolynomialInterpolation(da, z):
solution := solve(f=-z, z, explicit);
zz := [x1,x2,x3,x4];
sigma := symMonomial(zz); #sigma := [x1+x2+x3+x4, x1*x2+x1*x3+x1*x4+x2*x3+x2*x4+x3*x4, x1*x2*x3+x1*x2*x4+x1*x3*x4+x2*x3*x4, x1*x2*x3*x4]
sys1 := subs([x1=solution[1],x2=solution[2],x3=solution[3],x4=solution[4]], sigma[1]):
sys2 := subs([x1=solution[1],x2=solution[2],x3=solution[3],x4=solution[4]], sigma[2]):
sys3 := subs([x1=solution[1],x2=solution[2],x3=solution[3],x4=solution[4]], sigma[3]):
sys4 := subs([x1=solution[1],x2=solution[2],x3=solution[3],x4=solution[4]], sigma[4]):
da := [seq([i,close3[i][1]], i=1..5)];

with(Optimization):
LPSolve(sys1, {sys2}, assume = {nonnegative});

how to further remove _Z with explicit in two variables case?

da := [[1,m],[2,m2],[3,1],[4,2],[5,3],[6,4]];
f := PolynomialInterpolation(da, z):
solution := solve(f=-z, z, explicit);

Is there a library to draw state machine diagram from logic table in Maple?